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fit a 3d curve

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Elza
Elza 2011-4-14
回答： Sonali 2023-8-27
Dear all,
I am a beginner in Matlab and I need your help. Here is my problem: I have a cloud of data obtained by measurement. Thanks to those datas I have made a matrix(49x49) which allowed me to plot a paraboloid. I would like to fit this 3d curve based on data, but I don't know how to start. Could you please help me to find a way to solve this problem?
Sincerely,
Elza

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采纳的回答

Andrew Newell
Andrew Newell 2011-4-14
编辑：John Kelly 2014-6-12
If you have the Curve Fitting Toolbox, you could try interactive surface fitting.
EDIT: If you don't have it, you could try polyfitn, which you can download from the File Exchange.

更多回答（4 个）

Elza
Elza 2011-4-14
Many thanks for your answer. Actually I don't have this tool. Do you know an other way to do it?
Thanks a million.
Elza
Jarrod Rivituso
Jarrod Rivituso 2011-4-14
Could you cast it as a linear regression problem and then solve the equations using backslash? Some details:
Say we are trying to fit to an equation of the form
z = c1*f1(x,y) + c2*f2(x,y) + ...
where f1 and f2 are the basis functions of the linear equation, and c1,c2,etc. are the coefficients. You could write this as a matrix equation...
z = [f1(x,y) , f2(x,y) , ...] * [c1 ; c2 ; ...]
Here's an example in MATLAB with some data I made up...
%Define grid of x,y values
x = -1:0.01:1;
y = -1:0.01:1;
[X,Y] = meshgrid(x,y);
%Make up some data
data = X.^2 + 3*Y.^2 + 0.01*rand(size(X));
%Set the basis functions
f1 = ones(size(X));
f2 = Y.^2;
f3 = X.^2;
%Write as matrix equation
A = [f1(:),f2(:),f3(:)];
y = data(:);
%Solve for coefficients
coeffs = A\y
Elza
Elza 2011-4-20
Thanks for your help Jarrod, I'll try that and let you know if it works for me.
Many thanks
Sonali
Sonali 2023-8-27
Rt = 30.5;
area_ratio = 31.4754;
theta = 50;
theta_exit = 16.5;
theta_n = theta*pi/180;
k = 0.8;
Ln = k*(sqrt(area_ratio)-1)*Rt/tand(theta_exit);
% FIRST CURVE (FC)
% Angles for First Curve
Angle_FC = -(pi+(45*pi/180));
FC_step = (-pi/2-Angle_FC)/100;
theta_FC = (-3*pi/4):FC_step:(-pi/2);
% Coordinates for First Curve
x_FC = cos(theta_FC)*1.5*Rt;
y_FC = sin(theta_FC)*1.5*Rt+(1.5*Rt+Rt);
x_FC1 = x_FC';
y_FC1 = y_FC';
% SECOND CURVE (SC)
% Angle for Second Curve
Angle_SC = -pi/2;
SC_step = ((theta_n-pi/2)-Angle_SC)/100;
theta_SC = -pi/2:SC_step:(theta_n-pi/2);
% Coordinates for Second Curve
x_SC = cos(theta_SC)*0.382*Rt;
y_SC = sin(theta_SC)*0.382*Rt+(0.382*Rt+Rt);
x_SC1 = x_SC';
y_SC1 = y_SC';
% THIRD CURVE (TC)
% Coordinates for Third Curve
x_TC = cos(theta_n-pi/2)*0.382*Rt;
y_TC = sin(theta_n-pi/2)*0.382*Rt+(0.382*Rt+Rt);
% Exit Coordinates
y_exit = sqrt(area_ratio)*Rt;
matrix_y = [y_TC^2 y_TC 1; y_exit^2 y_exit 1; 2*y_TC 1 0];
matrix_x = [x_TC; Ln ;1/tan(theta_n)];
x_exit = matrix_y^-1*matrix_x;
a = x_exit(1,1);
b = x_exit(2,1);
c = x_exit(3,1);
y = y_TC:0.8:y_exit;
x = a*y.^2+b*y+c;
% Complete Coordinate
Rao_x = [x_FC x_SC x];
Rao_y = [y_FC y_SC y];
% Lower Geometry
Rao_y1 = -1*Rao_y;
%Coordinates
R_X = Rao_x';
R_Y = Rao_y';
Rao = [R_X R_Y];
% Figures
figure(1)
plot (Rao_x,Rao_y,'r','LineWidth',3)
hold on
plot (Rao_x,Rao_y1,'r','LineWidth',3)
hold of
I need this code To be generate in 3D model
can you please provide

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